Search found 781 matches

by wtf
Fri May 10, 2019 3:33 am
Forum: Logic and Philosophy of Mathematics
Topic: Possible consequences of falsifying the principle of explosion?
Replies: 86
Views: 2530

Re: Possible consequences of falsifying the principle of explosion?

PeteOlcott wrote:
Fri May 10, 2019 2:11 am
It sure as Hell makes much more sense than saying that every truth is logically
entailed by either falsehood or contradiction.
Avoiding the question I asked?
by wtf
Fri May 10, 2019 12:13 am
Forum: Logic and Philosophy of Mathematics
Topic: Possible consequences of falsifying the principle of explosion?
Replies: 86
Views: 2530

Re: Possible consequences of falsifying the principle of explosion?

I would correct it to conform to the English meaning this way: Logical implication p q p ⇒ q T T T T F F F T F F F F Isn't that what everyone else calls logical AND? Would you say that * 2 + 2 = 4 and George Washington is regarded as the father of his country. and * 2 + 2 = 4 THEREFORE George Washi...
by wtf
Wed May 08, 2019 12:47 am
Forum: Logic and Philosophy of Mathematics
Topic: Possible consequences of falsifying the principle of explosion?
Replies: 86
Views: 2530

Re: Possible consequences of falsifying the principle of explosion?

Instead of undecidable logic sentences "proving" incompleteness of formal systems they are merely rejected as derived from unsound deduction. That doesn't make any sense. If a sufficiently interesting system is consistent, it must necessarily contain closed wffs that can neither be proven nor dispr...
by wtf
Sat May 04, 2019 7:38 am
Forum: Logic and Philosophy of Mathematics
Topic: Converting formal proofs to conform to sound deduction
Replies: 30
Views: 1730

Re: Converting formal proofs to conform to sound deduction

Copyright ???? Pete Olcott It's not a legal copyright without a year. When I was a tech writer (a very long time ago) I learned to write "Copyright (C) 1920 Thomas Edison Company" in exactly that format. Just some free legal advice. And of course I'm not a lawyer and the law might have changed sinc...
by wtf
Fri May 03, 2019 4:23 am
Forum: Logic and Philosophy of Mathematics
Topic: Converting formal proofs to conform to sound deduction
Replies: 30
Views: 1730

Re: Converting formal proofs to conform to sound deduction

mortal adjective of a living human being often in contrast to a divine being subject to death. Thanks for clarifying your thinking. You are making the point that under your understanding of logic, we should analyze the word "mortal" and so forth. I'd submit that if you show the phrase "All men are ...
by wtf
Thu May 02, 2019 7:14 am
Forum: Logic and Philosophy of Mathematics
Topic: Tarski Undefinability Theorem Succinctly Refuted
Replies: 106
Views: 2376

Re: Tarski Undefinability Theorem Reexamined

... it says what it says - it does what it does. I think I'm going to go with ... not convinced that you have any idea what category theory is. It's no great shame. You could say something like, "Cool, I've heard about category theory but don't know much about it. Tell me more." Or even, "F*** you,...
by wtf
Wed May 01, 2019 12:54 am
Forum: Logic and Philosophy of Mathematics
Topic: Converting formal proofs to conform to sound deduction
Replies: 30
Views: 1730

Re: Converting formal proofs to conform to sound deduction

I mean it in the sense where "are" means ⇔ Oh well that explains your "all X are Y" remark. Classically "All men are mortal" means ==> and not <==>, we agree on that I hope. So if you said, "All X are Y and all Y are X" you'd at least have identity between sets. That would have been more clear to a...
by wtf
Wed May 01, 2019 12:46 am
Forum: Logic and Philosophy of Mathematics
Topic: Tarski Undefinability Theorem Succinctly Refuted
Replies: 106
Views: 2376

Re: Tarski Undefinability Theorem Reexamined

Logik wrote:
Wed May 01, 2019 12:02 am
wtf wrote:
Tue Apr 30, 2019 11:40 pm
What do you think about universal mapping properties?
It's a formalization of Equifinality.

https://en.wikipedia.org/wiki/Equifinality
You have not convinced me that when we talk about category theory we are talking about the same thing.
by wtf
Tue Apr 30, 2019 11:40 pm
Forum: Logic and Philosophy of Mathematics
Topic: Tarski Undefinability Theorem Succinctly Refuted
Replies: 106
Views: 2376

Re: Tarski Undefinability Theorem Reexamined

Logik wrote:
Sun Apr 28, 2019 12:21 pm
Category theory is pretty much how I think about the world. Start with highest level of abstraction, then decompose down to least complex elements.
What do you think about universal mapping properties?
by wtf
Tue Apr 30, 2019 11:27 pm
Forum: Logic and Philosophy of Mathematics
Topic: Converting formal proofs to conform to sound deduction
Replies: 30
Views: 1730

Re: Converting formal proofs to conform to sound deduction

Really? So when I say "All cats are mammals" that's the same as saying cats are isomorphic to mammals? OK. so you are using "are" to mean "subset of". Cool. We can play that game right until we get to the set of all sets. And then I am going to ask you.... This isn't just wrong on the facts, it's m...
by wtf
Tue Apr 30, 2019 11:03 pm
Forum: Logic and Philosophy of Mathematics
Topic: Converting formal proofs to conform to sound deduction
Replies: 30
Views: 1730

Re: Converting formal proofs to conform to sound deduction

To say ALL X are Y is to say "there is an isomorphism between X and Y". And that only works in formal systems. Really? So when I say "All cats are mammals" that's the same as saying cats are isomorphic to mammals? This isn't just wrong on the facts, it's meta-wrong. It's a category error. It's not ...
by wtf
Sat Apr 27, 2019 1:05 am
Forum: Logic and Philosophy of Mathematics
Topic: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)
Replies: 33
Views: 698

Re: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)

PeteOlcott wrote:
Sat Apr 27, 2019 1:02 am
I think these things through more deeply as I get more feedback.
I am gratified to have made my point.
by wtf
Sat Apr 27, 2019 12:33 am
Forum: Logic and Philosophy of Mathematics
Topic: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)
Replies: 33
Views: 698

Re: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)

If person Y could come up with some set of axioms such as PA that make their stipulation coherent (such as the distinction between Euclidean and non-Euclidean geometry) then it would be acceptable. I said nothing about PA. In fact these are one-sentence axiom systems . The entirety of the axiom sys...
by wtf
Fri Apr 26, 2019 11:52 pm
Forum: Logic and Philosophy of Mathematics
Topic: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)
Replies: 33
Views: 698

Re: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)

Person X stipulates the axiom 2 + 2 = 4. Person Y stipulates the axiom 2 + 2 = 5. Are both axioms true by virtue of being axioms? I think that most people would agree that person Y would be a liar for directly contradicting mutually agreed upon conventions. Then you agree that the truth value of a ...
by wtf
Fri Apr 26, 2019 7:10 pm
Forum: Logic and Philosophy of Mathematics
Topic: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)
Replies: 33
Views: 698

Re: Eliminating Undecidability and Incompleteness in Formal Systems (As simple as possible)

PeteOlcott wrote:
Fri Apr 26, 2019 5:55 pm
I know that my premises are true because they are semantic tautologies:
You ignored my question.

Person X stipulates the axiom 2 + 2 = 4.

Person Y stipulates the axiom 2 + 2 = 5.

Are both axioms true by virtue of being axioms?